It's one of the most prominent university 駅伝(Ekiden), which means relay marathon races, of the year held between Tokyo and 箱根(Hakone) on January 2nd and 3rd. 

The race is telecast on TV, only male runners are allowed to take part in this competition. They run from Tokyo to Hakone on January 2nd, and then they come back from Hakone to Tokyo on January 3rd. This two-day race from Tokyo to Hakone and back is separated into 5 sections on each day, due to slight variations in the courses, the first-day distance is 108km, while the distance on the second day is 109.9km. ( My penfriend from Japan told me about this race.)

Hakone Ekiden 2008

Some Japanese people spend their New Year holiday watching the marathon on TV.